\(\rho^{0} - \omega\) mixing in the presence of a weak magnetic field

Abstract.

We calculate the momentum dependence of the \(\rho^{0}-\omega\) mixing amplitude in vacuum with vector-nucleon-nucleon interaction in presence of a constant homogeneous weak background magnetic field. The mixing amplitude is generated by the nucleon-nucleon (NN) interaction and is thus driven by the neutron-proton mass difference in addition to the constant magnetic field. We find a significant effect of the magnetic field on the mixing amplitude. We also calculate the charge symmetry violating (CSV) NN potential induced by the magnetic field dependent mixing amplitude. The presence of the magnetic field influences the NN potential substantially which can have important consequences on highly magnetized astrophysical compact objects, such as magnetars. The most important observation of this work is that the mixing amplitude is non-zero, leading to a positive contribution to the CSV potential even if the proton and neutron masses are taken to be equal. We also show that with the inclusion of the anomalous magnetic moment of the nucleons, the anisotropic nature of the CSV potential gets enhanced even if the background magnetic field is weak.